Can physical system modeling be taught? Is it an art or a science?
Many engineers have little experience, and, therefore, little confidence in doing it. But physical system modeling, either applied to an existing system, or a concept in the design process, leads to thorough understanding, differentiates engineers, and gives companies a competitive advantage that leads to innovation.
There is a hierarchy of physical models possible in response to the question: Why am I modeling? Engineering judgment, and simplifying assumptions applied to the physical system, lead to the physical model, which must capture the essential multidisciplinary attributes of the physical system. A working knowledge of multidisciplinary physics is essential, and the simplest model that meets the need is always best.
Figure 1
Here are two examples. Figure 1 shows an internal combustion engine connected to an eddy-current dynamometer. The physical model is shown in Figure 2. The engine is considered a nonlinear angular velocity source (ϖE) modulated by the throttle setting θ(t). The main energy storage is associated with the rotating inertia JE, lumped at the output of the engine shaft. The torque transmission shaft has compliance and energy dissipation, and is modeled with a rotational spring KS and rotational damper BS. The shaft inertia is neglected.
Figure 2
The dynamometer consists of a toothed rotor JR that rotates (ϖR) in the magnetic field created by passing current (t) through the stator windings. A voltage is induced in the conductive rotor rotating in the stator magnetic field (Faraday’s Law). This induced voltage creates eddy currents in the rotor that generate a magnetic field (Ampere’s Law), which opposes the stator magnetic field (Lenz’s Law).
The stator inertia JS, mounted in trunnion bearings, is free to rotate, but is restrained by a torque arm to measure the torque developed. The spring K and damper B represent the compliance and energy dissipation associated with the torque measurement.
Figure 3
Figure 3 shows a portion of a web-handling system between two sets of driven rolls. A physical model is the first step to predicting and controlling both the tension and velocity of the web. What is most interesting here is that a failure to understand the fundamental physics of web transport led to inaccurate modeling for many years.
The Law of Conservation of Mass is applied to a control volume encompassing the web span, where the physical model allows for the transport of strain ε from the upstream web span to the downstream span, an essential characteristic validated by experimental observations. T is the web tension, assumed constant in any web span of length L.
Successful physical modeling requires a fundamental understanding of multidisciplinary physics, and a commitment to do it without falling back on the old design-build-test approach. This is the most direct path to innovation.
Modeling of physical systems was not taught in school. I claim it's an art. When I have performed this "art", only other engineers who were intelligent enough to have done it themselves have understood. Experiance? No. As a new grad years ago, I had to model a motor driver / antenna / radar system. I had no experiance but I pulled it off. It required understanding that a derivative is the change of parameter A w.r.t. parameter B. Hmm, I couldn't understand why that concept was so difficult to grasp by others. One of the closed-loop parameters was the angle of the target. This was in radians. Another parameter was the electrical phase lag angle of the motor current. This was in degrees. "You can't mix degrees with radians" some people shouted." I remember this vividy from decades ago. They were actually angry. "You certainly can", I replied. Luckily for this new grad, there were other engineers in the room who understood simple principles of math and the model was accepted.
Scott, well said. Too many times, our engineering team delivered our product design on time, on cost and on spec. but the product didn't sell as well as anticipated. Why? Because the buying behaviors as you stated below were also not properly or accurately 'modeled'.
I think taking time to write down the model can help insure that we don't miss one important detail which is ususally what happens when we do it in our head.
Interesting discussions. As a mechanical engineer who has made the transition into marketing and product development I can say that modeling (i.e. the mathmatical representation of the real world) is not confined to physical systems. Buying behavior, pricing scenarios, market response to financial pressures all lend themselves to modeling. Having the experience to look for these associations and the understanding to apply the correct modeling dynamics comes from my engineering background.
Being able to procede without doing the modeling, or being able to do the modeling without doing all of the math, and getting it right, is the vaue of experienc, at least potentially the value. Knowing where you can't get away with assumptions is the biggest value of experience.
I agree. In many cases, the real numbers needed for these equations must be empirically determined through experimental measurement (and that can get quite tedious, time-consuming and expensive when a project is on a fast-track). Sometimes engineers want to take the time to run experiments to properly model the system, but management may not have the patience or commitment to allocate the needed resources and or allow the time to do it right.
The ability to produce an adequate model is very useful, but accuracy is omportant. One additional advantage of producing the model is that it serves as a "reality check" as it helps to avoid missing pieces and details.
BUT attaching real numbers to a model does get quite tedious, while some of them can be looked up, othhers must be calculated.THAT can be very tedious indeed, I have found in the past.
I agree that the ability to physically model systems is a valuable skill. Having a good physical model can shed light on different areas of the design and accelerate system optimization and solution break throughs.
These skills are quite complicated to master and I think the main keys are gaining experience through practice and also having a good mentor.
This is all very detailed and complex. Most engineers I know have not used math beyond algebra or geometry in their day job careers. However, when faced with a problem, most engineers know where to look up info like the above. (The old cliche)
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